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**EEG-MEG source reconstruction**

rIFG lA1 rA1 lSTG rSTG Jean Daunizeau Wellcome Trust Centre for Neuroimaging 08 / 05 / 2009

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**EEG/MEG data sensor locations structural MRI anatomical templates**

spatial denormalisation individual meshes data convert epoching BEM forward modelling trials gain matrix baseline correction averaging over trials low pass filter (20Hz) evoked responses cortical sources inverse modelling 1st level contrast standard SPM analysis

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**EEG/MEG data sensor locations structural MRI standard SPM analysis**

individual meshes cortical sources spatial denormalisation structural MRI anatomical templates data convert epoching BEM forward modelling trials gain matrix baseline correction averaging over trials low pass filter (20Hz) evoked responses inverse modelling 1st level contrast

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**Bayesian inference applied to distributed source reconstruction **

Introduction Forward Inverse Bayes SPM Conclusion Introduction Forward problem Inverse problem Bayesian inference applied to distributed source reconstruction SPM variants of the EEG/MEG inverse problem Conclusion En premier lieu, j’introduirais les

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**Forward and inverse problems: definitions**

Introduction Forward Inverse Bayes SPM Conclusion Forward and inverse problems: definitions Forward problem = modelling Inverse problem = estimation of the model parameters

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**Physical model of bioelectrical activity**

Introduction Forward Inverse Bayes SPM Conclusion Physical model of bioelectrical activity current dipole

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**Fields propagation through head tissues**

Introduction Forward Inverse Bayes SPM Conclusion Fields propagation through head tissues noise dipoles gain matrix Y = KJ + E1 measurements

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**An ill-posed problem Jacques Hadamard (1865-1963) Existence Unicity**

Introduction Forward Inverse Bayes SPM Conclusion An ill-posed problem Jacques Hadamard ( ) Existence Unicity Stability

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**An ill-posed problem Jacques Hadamard (1865-1963) Existence Unicity**

Introduction Forward Inverse Bayes SPM Conclusion An ill-posed problem Jacques Hadamard ( ) Existence Unicity Stability

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**Imaging solution: cortically distributed dipoles**

Introduction Forward Inverse Bayes SPM Conclusion Imaging solution: cortically distributed dipoles Signal sensible en EEG !

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**Imaging solution: cortically distributed dipoles**

Introduction Forward Inverse Bayes SPM Conclusion Imaging solution: cortically distributed dipoles

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**(regularization term)**

Introduction Forward Inverse Bayes SPM Conclusion Regularization Data fit Adequacy with other modalities Spatial and temporal constraints data fit constraint (regularization term) W = I : minimum norm method W = Δ : LORETA (maximum smoothness)

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**Priors and posterior likelihood priors posterior model evidence**

Introduction Forward Inverse Bayes SPM Conclusion Priors and posterior likelihood priors posterior model evidence

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**Hierarchical generative model**

Introduction Forward Inverse Bayes SPM Conclusion Hierarchical generative model source level sensor level Q : (known) variance components (λ,μ) : (unknown) hyperparameters

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**Hierarchical generative model: graph**

Introduction Forward Inverse Bayes SPM Conclusion Hierarchical generative model: graph λ1 λq J μ1 μq Y

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**Restricted Maximum Likelihood (ReML)**

Introduction Forward Inverse Bayes SPM Conclusion Restricted Maximum Likelihood (ReML) generative model M average over J model associated with F

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**Imaging source reconstruction in SPM**

Introduction Forward Inverse Bayes SPM Conclusion Imaging source reconstruction in SPM generative model M IID COH ARD/GS prior covariance structure

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**Source reconstruction for group studies**

Introduction Source reconstruction for group studies Forward Inverse Bayes SPM Conclusion Group studies canonical meshes!

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**Equivalent Current Dipoles (ECD)**

Introduction Forward Inverse Bayes SPM Conclusion Equivalent Current Dipoles (ECD) soft symmetry constraints! Somesthesic stimulation (evoked potential) ECD moments prior precision ECD positions prior precision ECD moments ECD positions measurement noise precision EEG/MEG data

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**Dynamic Causal Modelling (DCM)**

Introduction Forward Inverse Bayes SPM Conclusion Dynamic Causal Modelling (DCM) macroscopic scale mesoscopic scale microscopic scale system of ensembles ensemble (105~106 neurons) neuron mean-field response (due to ensemble dispersion) excitatory interneurons pyramidal cells effective connectivity (due to synaptic density) interneurons inhibitory

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**• EEG/MEG source reconstruction: 1. forward problem; **

Introduction Forward Inverse Bayes SPM Conclusion • EEG/MEG source reconstruction: 1. forward problem; 2. inverse problem (ill-posed). • Prior information is mandatory to solve the inverse problem. • Bayesian inference is well suited for: 1. introducing such prior information… 2. … and estimating their weight wrt the data 3. providing us with a quantitative feedback on the adequacy of the model.

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**individual reconstructions in MRI template space**

Introduction Forward Inverse Bayes SPM Conclusion R L individual reconstructions in MRI template space RFX analysis p < 0.01 uncorrected R L SPM machinery

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**Guillaume Magic Flandin**

Introduction Forward Inverse Bayes SPM Conclusion Many thanks to… Karl Friston Stephan Kiebel Jeremie Mattout Christophe Phillips Vladimir Litvak Guillaume Magic Flandin

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